| In the background of aging population, the problem of supporting old people have been paid much attention by every country. Furthermore ,the problem of supporting old and rural people is more important and urgent. The new rural social pension insurance in our country is called the NRSPI in short. In order to be clear about whether the NRSPI can achieve the target of insuring the basic life of the insured or not, the replacement rate of the NRSPI should be studied urgently. However, the majority of domestic articles had been carried by qualitative analyzing, not by quantitative analyzing from the condition of research in china. Although some scholars had conducted research on the NRSPI from the perspective of actuarial Science,but the model in these researches is relatively simple, which is not suitable for the use in complex social environment. Based on the above issues, this paper studies the replacement rate from the following sections of the NRSPI.Firstly, the replacement rate of the NRSPI is derived under the fixed interest rate, then the sensitivity analysis to the several factors is conducted.Secondly, considering the impact of various factors on interest rate fluctuation, the function of interest force is built by adopting the Wiener process, reflecting Brownian motion,Gauss process, Poisson process.Thirdly, the expectation of the supply replacement rate is derived under the hypothesis of the several functions of interest force ; Monte Carlo simulation is performed through numerical examples, then the expectation ,the variance , the diagram of empirical distribution function and the diagram of empirical density function is obtained.Finally, the simulation and predict of the replacement rate of the demand in rural residents is conducted by the software of Eviews ; then by comparing the replacement rate of the demand and supply, the result that whether the NRSPI can achieve the target of insuring the basic life of the insured or not is obtained. |
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